Page 22 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions

HOTS Example 2 Solution
The diagram below shows a bucket in the Volume of cylinder
shape of a cylinder which is fully-filled with 22   2
21
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water and another container in the shape of = 7 × 2 × 18
a right prism with a rectangular base ABCD. = 6 237 cm 3
The trapezium ABFE is the uniform cross
section of the right prism. All the water Volume of water in the right prism = 6 237 cm 3
from the bucket is poured into the container 3 1 Form 4
3 × (14 + 10)x × (5x – 27) = 6 237
and filled of the container. 4 2
4 9x(5x – 27) = 6 237
H G x(5x – 27) = 693
2
x cm 5x – 27x – 693 = 0
14 cm D C
(–27)
2
E x = –(–27) ± – 4(5)(–693)
18 cm F (5x – 27) cm 2(5)
A B x = 27 ±14 589
21 cm 10 cm 10
x = –9.378 (ignored) or x = 14.78
22
Using π = , calculate the value of x.
7 Then, x = 14.78

SPM PRACTICE
SPM PRACTICE

Paper 1 5. Find the range of values of p if the
quadratic equation x – 6px + p = 0 has
2
1. Given the quadratic equation no roots.
x + px = 3x – 4 has two different roots, 2
2
find the range of values of k. 6. The quadratic equation px + qx + r = 0
6
3
2. Given 7 is one of the roots of the has roots – and 5 . Find the values of
7
4
quadratic equation 5(x + k) = 405, p, q and r.
2
where k is a constant. Find the values of 7. Given α and β are the roots of the
k. quadratic equation 2x – 9x + 9 = 0.
2
3. Given a quadratic equation Form a quadratic equation that has roots
β
kx – 3hx + 4k = 0 where k and h are α and .
2
constants, has only one x-intercept. Find 3 3
h : k.
8. (a) Express 4x(x – 5) = (3x – 1)(x + 1)
4. Given one of the roots of the equation in general form.
x + (3p – 4)x – p = 0, where p is a (b) Hence, solve the quadratic equation
2
2
constant, is negative to another root. and give the answers correct to 4
Find the value of the product of the significant figures.
roots.
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